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Difficult puzzle

 
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leocar



Joined: 04 Mar 2010
Posts: 12
PostPosted: Thu Jun 03, 2010 9:25 am    Post subject: Difficult puzzle Reply with quote
Hi, I came across this puzzle but got stuck very early. Can someone please help me with the next step as I am at a loss. Thank you.
Leo


Code:

+----------------+-------------+----------------+
| 7    48   9    | 1    2  6   | 48   5    3    |
| 1    68   5    | 47   3  47  | 2689 2689 689  |
| 46   2    3    | 8    9  5   | 467  467  1    |
+----------------+-------------+----------------+
| 356  9    167  | 456  8  134 | 467  467  2    |
| 568  1567 4    | 2    56 19  | 3    6789 5689 |
| 2    356  68   | 4569 7  349 | 4689 1    5689 |
+----------------+-------------+----------------+
| 4689 467  678  | 679  1  2   | 5    3    689  |
| 3689 367  2678 | 5679 56 789 | 1    2689 4    |
| 5689 156  1268 | 3    4  89  | 2689 2689 7    |
+----------------+-------------+----------------+
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu Jun 03, 2010 12:15 pm    Post subject: Reply with quote
The next step is a hidden pair in B4. After that, I don't know.

Keith
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
PostPosted: Thu Jun 03, 2010 1:54 pm    Post subject: Reply with quote
You can place 3 in r8c2 using the contradiction:

r8c2 ≠3 => r8c1 = 3 => r4c1 ≠ 3 => r4c6 = 3 => r4c3 =1 => r5c2 =7 => r9c2 = 1 => r6c2 =5 => r8c2 = 3.

This gives

Code:
+---------------------------------------------+
| 7    48  9    | 1    2  6   | 48   5    3   |
| 1    68  5    | 47   3  47  | 2689 2689 689 |
| 46   2   3    | 8    9  5   | 467  467  1   |
-----------------------------------------------
| 3    9   17   | 5    8  14  | 467  467  2   |
| 568  17  4    | 2    6  19  | 3    789  589 |
| 2    56  68   | 49   7  3   | 489  1    589 |
-----------------------------------------------
| 4689 467 678  | 679  1  2   | 5    3    689 |
| 689  3   2678 | 5679 5  789 | 1    2689 4   |
| 5689 156 1268 | 3    4  89  | 2689 2689 7   |
+---------------------------------------------+

There are now conjugates with respect to 6 in b1 and c9. As they line up in r2, 6 can be eliminated from r7c1. It may also be eliminated from r8c1 using the contradiction

r8c1 = 6 => r8c4 ≠ 6 => r7c4 = 6 => r7c9 ≠ 6 => r2c9 = 6 => r2c2 = 8 => r3c1 = 6

We now have

Code:
+-------------------------------------------+
| 7    48  9    | 1   2 6   | 48   5    3   |
| 1    68  5    | 47  3 47  | 2689 2689 689 |
| 46   2   3    | 8   9 5   | 467  467  1   |
---------------------------------------------
| 3    9   17   | 5   8 14  | 467  467  2   |
| 58   17  4    | 2   6 19  | 3    789  589 |
| 2    56  68   | 49  7 3   | 489  1    589 |
---------------------------------------------
| 489  467 678  | 679 1 2   | 5    3    689 |
| 89   3   2678 | 679 5 789 | 1    2689 4   |
| 5689 156 1268 | 3   4 89  | 2689 2689 7   |
+-------------------------------------------+

when 4 can be placed in r7c1 using the contradiction

r7c1 ≠ 4 => r7c2 = 4 => r5c2 = 7 => r9c2 = 1 => r9c1 = 5 => r3c1 = 6 => r7c1 = 4.

The rest is intermediate rather than easy but you don’t need any more chains unless you wish to use them.

Steve
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